General Relativity and Quantum Cosmology (gr-qc)

Abstract: Three - dimensional static and spinning black hole solutions of the Einstein-Klein-Gordon system are obtained for a particular scalar field configuration. At large distances, and for small scalar field, the solutions reduce to the BTZ black hole. The scalar field dresses the black hole with secondary scalar hair, since the scalar charge is related to the conserved black hole mass and is not an independent charge. A self interacting potential is included, containing a mass term that is above the Breitenlohner-Freedman bound in three dimensions. Independence of the scalar potential from the conserved black hole charges, imposes fixed mass and angular momentum to scalar charge ratios. The thermodynamic properties as well as the energy conditions of the black hole are analysed.

Abstract: Hawking's quasi-local energy definition quantifies the energy enclosed by a spacelike 2-sphere in terms of the amount of lightbending on the sphere caused by the energy distribution inside the sphere. This paper establishes for the first time a direct connection between the formal mathematical definition of a quasi-local energy and observations, in the context of cosmological perturbation theory. This is achieved by studying the Hawking Energy of spherical sections of the past lightcone of a cosmic observer in a perturbed Friedmann-Lema\^{i}tre spacetime. We express the Hawking Energy in terms of gauge-invariant perturbation variables and comment on the cosmic observables needed to in principle measure it. We then calculate its angular power spectrum and interpret its contributions.

Abstract: Gravitational waves can generate electromagnetic effects inside a strong electric or magnetic field within the Standard Model and general relativity. Here we propose using a quarterly split cavity and LC-resonance circuit to detect a high-frequency gravitational wave from 0.1 MHz to GHz. We perform a full 3D simulation of the cavity's signal for sensitivity estimate. Our sensitivity depends on the coherence time scale of the high-frequency gravitational wave sources and the volume size of the split cavity. We discuss the resonant measurement schemes for narrow-band gravitational wave sources and also a non-resonance scheme for broadband signals. For a meter-sized split cavity under a 14 Tesla magnetic field, the LC resonance enhanced sensitivity to the gravitational wave strain is expected to reach $h\sim 10^{-20}$ around $10$ MHz.